
The FL spectral problem (REF ) is not the Zakharov-Shabat type spectral
problem due to the multiplication by \(k\)  in the matrix potential \(kP_x\)  and the time part () admits spectral singularity at \(k=0\) .
To control the behavior of the eigenfunction \(\psi (k)\)  as \(k\rightarrow \infty \)  and \(k\rightarrow 0\)  in constructing the solution \(u(x,t)\)  to the FL equation \((\ref {cs})\) , we consider two different asymptotic expansions respectively at the singularities \(k=0\)  and \(k=\infty \) .
Here, we recall existing results on the constructing the RH problem, which can be found in [1]}, [2]}.
